I have recently gone through this process. My contract of employment was terminated last July but it was actually December when I actually received my NHS pension. I did receive 2 months backdated payments.
I was lucky enough to get tier 2 pension, which is the better one as you get paid 2/3 of what you would have been paid if you had worked until 62. It was very stressful as obtaining your pension this way is not guaranteed you do have to fight for it.
Try and get as much evidence about your condition and how it affects you from your consultant, GP, physiotherapist, occupational health doctor etc as this really helps. My manager also put in a written recommendation for me.
As regards difference in pension payments, yes there is. If you telephone NHS pensions they will give you an approximate figure for both.
Good luck x